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Math Help - Interval estimation of an exponential function

  1. #1
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    Interval estimation of an exponential function

    Hi, I was trying to solve this question (which is assigned to me) from Stapleton's book (7.7.1.a).

    I have a solution which is not correct but I couldn't understand where am I wrong? And couldn't understand the solution of the author.

    I hope you can see the following gif image.

    Interval estimation of an exponential function-eqn3.gif



    Thank you in advance.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by bilgedama View Post
    Hi, I was trying to solve this question (which is assigned to me) from Stapleton's book (7.7.1.a).

    I have a solution which is not correct but I couldn't understand where am I wrong? And couldn't understand the solution of the author.

    I hope you can see the following gif image.

    Click image for larger version. 

Name:	Eqn3.gif 
Views:	31 
Size:	24.7 KB 
ID:	20693



    Thank you in advance.
    All you need to do is find $$\theta_{0.9} such that:

    P(X\ge x|\theta_{0.9})<0.1

    where $$x is the observation, which is the solution for $$\theta_{0.9} to:

    e^{-x/\theta_{0.9}}=0.9

    which is:

    \displaystyle \theta_{0.9}=\frac{x}{\ln(0.9)}

    CB
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  3. #3
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    Thank you for the answer. Which step of my solution is not correct?
    I suspect my result about the distribution of T/(2lamba) is not correct. ?
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